CERTAINLY IT'S POSSIBLE to cut the federal budget further. And it's necessary. The Gramm-Rudman-Hollings machinery is now in gear, and the budget that President Reagan proposes to Congress in February will probably call for more than $60 billion in deficit reductions next year. He apparently intends to take nearly all of it from that one-third of the budget that is neither defense, interest nor Social Security and Medicare. Within that one-third, there are still programs -- most of them survivors from less straitened times -- that could indeed go.

For one example, general revenue sharing can be allowed to pass into history -- as Congress acknowledged in the reconciliation bill that it didn't quite pass in December. For another example, the Economic Development Administration, offering additional grants to state and local governments, would not be greatly missed. Nor would UDAG, the urban development action grant program; it supports cities' renewal plans, frequently for projects that might better find commercial financing. The president was right last year to call for an end to the Small Business Administration, and no doubt he will call for it again. The question is not what's desirable but, in a year of severe constraint, what's indispensable. The list of dispensables could be carried to greater length.

But when you add it all up, you are not going to come up with a great deal of money. Even pressing all the limits, it's hard to see as much as $15 billion in legitimate and plausible budget cuts here for next year. After all, this most vulnerable one-third of the budget has been reviewed repeatedly by the budget-balancers, beginning in the Carter administration. It is ground that has been raked over and over. That part of the budget currently comes to abt $320 billion, and since the beginning of the Reagan administration it has sustained more than $60 billion in cuts. If cutting goes much further in this area, it will begin to erode the ability of the government even to carry out the basic public functions necessary to keep itself operating effectively -- to collect the taxes, enforce the laws, administer justice and the rest.

And while some parts of the budget can still be reduced, some other parts of it urgently need to be expanded. The poorest one-fifth of the American people are living in privation that has greatly increased in recent years, and half of that one-fifth are children. Their condition stands as evidence that cuts in family support, nutrition and health outlays have already gone too far.

That's why no part of the budget should be considered off limits. Although Mr. Reagan has adamantly refused to consider it, Social Security can be trimmed without injustice to recipients. Congress has moved a couple of times toward postponing or diminishing the cost-of-living adjustments. That's a bad idea, for the impact would fall equally on the poorest and the wealthiest of recipients alike. But how about taxing Social Security a bit more broadly? Half of Social Security benefits are now taxable above a certain income threshold -- $32,000 a year, in the case of a couple. Why not abolish that threshold? If the same sound principle were applied to unemployment compensation and workers' compensation as well, all together it would raise $4 billion next year and much more in the years beyond. But all of that would still leave the total deficit reduction far less than half of the huge amount required by Gramm-Rudman-Hollings.

As for defense, it's possible to debate whether the Pentagon is spending its money on precisely the right things. It's reasonable to say that defense spending is adequate for present circumstances and may not require any further increase in real terms -- that is, after inflation. But cutting the defense budget would be altogether unwise. Another way will have to be found to get the deficit under control.

There is only one other way: to raise taxes. A tax increase is now mandatory. It needs to be very large -- in the range of $150 billion a year, phased in over the next several years. It does not have to be big enough to reduce the federal deficit to zero, least of all with the unemployment rate still hovering around 7 percent. But it has to be big enough to bring the deficit down rapidly, convincingly and permanently.

Over the months ahead, a simple test will distinguish serious budget strategy from posturing. Any serious strategy will require a tax increase sufficient to pay for national defense, social progress and the other public responsibilities that Americans want their federal government to uphold. Any budget plan that omits that tax is not serious. The arithmetic permits no detour around that reality.

There is a way out of the dangers into which the continuing gigantic budget deficits have brought the country. But there is only one way, and to take advantage of it President Reagan and Congress will have to move rapidly and forcefully.